Spin glasses in the non-extensive regime

TL;DR

This paper uses Monte Carlo simulations to investigate long-range spin glasses in the non-extensive regime, providing evidence that their transition temperatures match those of infinite-range models, confirming longstanding conjectures.

Contribution

The study offers numerical validation that non-extensive long-range spin glasses share transition temperatures with their infinite-range counterparts, extending the conjecture to diluted models.

Findings

Transition temperatures match those of infinite-range models.

Monte Carlo simulations support the conjecture.

Results apply to both regular and diluted long-range spin glasses.

Abstract

Spin systems with long-range interactions are "non-extensive" if the strength of the interactions falls off sufficiently slowly with distance. It has been conjectured for ferromagnets, and more recently for spin glasses, that, everywhere in the non-extensive regime, the free energy is exactly equal to that for the infinite range model in which the characteristic strength of the interaction is independent of distance. In this paper we present the results of Monte Carlo simulations of the one-dimensional long-range spin glasses in the non-extensive regime. Using finite-size scaling, our results for the transition temperatures are consistent with this prediction. We also propose, and provide numerical evidence for, an analogous result for diluted long-range spin glasses in which the coordination number is finite, namely that the transition temperature throughout the non-extensive regime is equal to that of the infinite-range model known as the Viana-Bray model.